Understanding preferred leg stiffness and layered control strategies for locomotion

Despite advancement in the field of robotics, current legged robots still cannot achieve the kind of locomotion stability animals and humans have. In order to develop legged robots with greater stability, we need to better understand general locomotion dynamics and control principles. Here we demonstrate that a mathematical modeling approach could greatly enable the discovery and understanding of general locomotion principles. ^ It is found that animal leg stiffness when scaled by its weight and leg length falls in a narrow region between 7 and 27. Rarely in biology does such a universal preference exist. It is not known completely why this preference exists. Here, through simulation of the simple actuated-SLIP model, we show that the biological relative leg stiffness corresponds to the theoretical minimum of mechanical cost of transport. This strongly implies that animals choose leg stiffness in this region to reduce energetic cost. In addition, it is found that the stability of center-of-mass motion is also optimal when biological relative leg stiffness values are selected for actuated-SLIP. Therefore, motion stability could be another reason why animals choose this particular relative leg stiffness range. ^ We then extended actuated-SLIP by including realistic trunk pitching dynamics. At first, to form the Trunk Spring-Loaded Inverted Pendulum (Trunk-SLIP) model, the point mass of actuated-SLIP is replaced by a rigid body trunk while the leg remains massless and springy. It is found that exproprioceptive feedback during the flight phase is essential to the overall motion stability including trunk pitching. Either proprioceptive or exproprioceptive feedback during stance could generate stable running motion provided that exproprioceptive feedback is used during flight. When both kinds of feedback are used during stance, the overall stability is improved. However, stability with respect to speed perturbations remains limited. ^ Built upon Trunk-SLIP, we develop a model called extended Trunk-SLIP with trunk and leg masses. We then develop a hierarchical control strategy where different layers of control are added and tuned. When each layer is added, the overall motion stability is improved. This layer by layer strategy is simple in nature and allows quick controller design and tuning as only a limited number of control parameters needs to be added and tuned at each step. In the end, we propose a future control layer where the commanded speed is controlled to achieve a higher level target such as might be needed during smooth walking to running transitions. ^ In summary, we show here that the simple actuated-SLIP model is able to predict animal center-of-mass translation stability and overall mechanical cost of transport. More advanced models are then developed based upon actuated-SLIP. With a simple layer by layer control strategy, robust running motion can be discovered. Overall, this knowledge could help better understand locomotion dynamics in general. In addition, the developed control strategy could, in principle be applied to future hip based legged robot design

Modular Hopping and Running via Parallel Composition

Though multi-functional robot hardware has been created, the complexity in its functionality has been constrained by a lack of algorithms that appropriately manage flexible and autonomous reconfiguration of interconnections to physical and behavioral components. Raibert pioneered a paradigm for the synthesis of planar hopping using a composition of ``parts\u27\u27: controlled vertical hopping, controlled forward speed, and controlled body attitude. Such reduced degree-of-freedom compositions also seem to appear in running animals across several orders of magnitude of scale. Dynamical systems theory can offer a formal representation of such reductions in terms of ``anchored templates,\u27\u27 respecting which Raibert\u27s empirical synthesis (and the animals\u27 empirical performance) can be posed as a parallel composition. However, the orthodox notion (attracting invariant submanifold with restriction dynamics conjugate to a template system) has only been formally synthesized in a few isolated instances in engineering (juggling, brachiating, hexapedal running robots, etc.) and formally observed in biology only in similarly limited contexts. In order to bring Raibert\u27s 1980\u27s work into the 21st century and out of the laboratory, we design a new family of one-, two-, and four-legged robots with high power density, transparency, and control bandwidth. On these platforms, we demonstrate a growing collection of $\{$body, behavior$\}$ pairs that successfully embody dynamical running / hopping ``gaits\u27\u27 specified using compositions of a few templates, with few parameters and a great deal of empirical robustness. We aim for and report substantial advances toward a formal notion of parallel composition---embodied behaviors that are correct by design even in the presence of nefarious coupling and perturbation---using a new analytical tool (hybrid dynamical averaging). With ideas of verifiable behavioral modularity and a firm understanding of the hardware tools required to implement them, we are closer to identifying the components required to flexibly program the exchange of work between machines and their environment. Knowing how to combine and sequence stable basins to solve arbitrarily complex tasks will result in improved foundations for robotics as it goes from ad-hoc practice to science (with predictive theories) in the next few decades

Exploiting inherent robustness and natural dynamics in the control of bipedal walking robots

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (p. 115-120).Walking is an easy task for most humans and animals. Two characteristics which make it easy are the inherent robustness (tolerance to variation) of the walking problem and the natural dynamics of the walking mechanism. In this thesis we show how understanding and exploiting these two characteristics can aid in the control of bipedal robots. Inherent robustness allows for the use of simple, low impedance controllers. Natural dynamics reduces the requirements of the controller. We present a series of simple physical models of bipedal walking. The insight gained from these models is used in the development of three planar (motion only in the sagittal plane) control algorithms. The first uses simple strategies to control the robot to walk. The second exploits the natural dynamics of a kneecap, compliant ankle, and passive swing-leg. The third achieves fast swing of the swing-leg in order to enable the robot to walk quickly (1.25m). These algorithms are implemented on Spring Flamingo, a planar bipedal walking robot, which was designed and built for this thesis. Using these algorithms, the robot can stand and balance, start and stop walking, walk at a range of speeds, and traverse slopes and rolling terrain. Three-dimensional walking on flat ground is implemented and tested in simulation. The dynamics of the sagittal plane are sufficiently decoupled from the dynamics of the frontal and transverse planes such that control.-of each can be treated separately. We achieve three-dimensional walking by adding lateral balance to the planar algorithms. Tests of this approach on a real three-dimensional robot will lead to a more complete understanding of the control of bipedal walking in robots and humans.by Jerry E. Pratt.Ph.D

Magnetorheological Variable Stiffness Robot Legs for Improved Locomotion Performance

In an increasingly automated world, interest in the field of robotics is surging, with an exciting branch of this area being legged robotics. These biologically inspired robots have leg-like limbs which enable locomotion, suited to challenging terrains which wheels struggle to conquer. While it has been quite some time since the idea of a legged machine was first made a reality, this technology has been modernised with compliant legs to improve locomotion performance. Recently, developments in biological science have uncovered that humans and animals alike control their leg stiffness, adapting to different locomotion conditions. Furthermore, as these studies highlighted potential to improve upon the existing compliant-legged robots, modern robot designs have seen implementation of variable stiffness into their legs. As this is quite a new concept, few works have been published which document such designs, and hence much potential exists for research in this area. As a promising technology which can achieve variable stiffness, magnetorheological (MR) smart materials may be ideal for use in robot legs. In particular, recent advances have enabled the use of MR fluid (MRF) to facilitate variable stiffness in a robust manner, in contrast to MR elastomer (MRE). Developed in this thesis is what was at the time the first rotary MR damper variable stiffness mechanism. This is proposed by the author for use within a robot leg to enable rapid stiffness control during locomotion. Based its mechanics and actuation, the leg is termed the magnetorheological variable stiffness actuator leg mark-I (MRVSAL-I). The leg, with a C-shaped morphology suited to torque actuation is first characterised through linear compression testing, demonstrating a wide range of stiffness variation. This variation is in response to an increase in electric current supplied to the internal electromagnetic coils of the MR damper. A limited degrees-of-freedom (DOF) bipedal locomotion platform is designed and manufactured to study the locomotion performance resulting from the variable stiffness leg. It is established that optimal stiffness tuning of the leg could achieve reduced mechanical cost of transport (MCOT), thereby improving locomotion performance. Despite the advancements to locomotion demonstrated, some design issues with the leg required further optimisation and a new leg morphology

Vertical hopper compositions for preflexive and feedback-stabilized quadrupedal bounding, pacing, pronking, and trotting

This paper applies an extension of classical averaging methods to hybrid dynamical systems, thereby achieving formally specified, physically effective and robust instances of all virtual bipedal gaits on a quadrupedal robot. Gait specification takes the form of a three parameter family of coupling rules mathematically shown to stabilize limit cycles in a low degree of freedom template: an abstracted pair of vertical hoppers whose relative phase locking encodes the desired physical leg patterns. These coupling rules produce the desired gaits when appropriately applied to the physical robot. The formal analysis reveals a distinct set of morphological regimes determined by the distribution of the body’s inertia within which particular phase relationships are naturally locked with no need for feedback stabilization (or, if undesired, must be countermanded by the appropriate feedback), and these regimes are shown empirically to analogously govern the physical machine as well. In addition to the mathematical stability analysis and data from physical experiments we summarize a number of extensive numerical studies that explore the relationship between the simple template and its more complicated anchoring body models. For more information: Kod*la

Biologically-plausible six-legged running : control and simulation

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.Includes bibliographical references (p. 63-66).This thesis presents a controller which produces a stable, dynamic 1.4 meter per second run in a simulated twelve degree of freedom six-legged robot. The algorithm is relatively simple; it consists of only a few hand-tuned feedback loops and is defined by a total of 13 parameters. The control utilizes no vestibular-type inputs to actively control orientation. Evidence from perturbation, robustness, motion analysis, and parameter sensitivity tests indicate a high degree of stability in the simulated gait. The control approach generates a run with an aerial phase, utilizes force information to signal aerial phase leg retraction, has a forward running velocity determined by a single parameter, and couples stance and swing legs using angular momentum information. Both the hypotheses behind the control and the resulting gait are argued to be plausible models of biological locomotion.by Matthew David Malchano.M.Eng

Template-based control of the bipedal robot ATRIAS

This thesis details the derivation and application of template-based controls on a bipedal robot, as well as a description of the software framework that enabled experimentation. The software framework uses a combination of open-source tools including ROS, OROCOS, EtherCAT, and Xenomai to create a real-time environment for the controllers. The first controller makes the robot (ATRIAS) walk as if it was the Spring Loaded Inverted Pendulum (SLIP) model. This demonstrates that ATRIAS, which was designed to be as close to the SLIP model as possible, can behave similarly to the reduced-order model. While the first controller is implemented with a torso that is mechanically fixed in place, the second controller handles an unlocked torso, which adds another degree of freedom. This controller is implemented based on a Torso SLIP (TSLIP) reduced-order model. The controller imposes a Virtual Pivot Point (VPP) by redirecting ground reaction forces to a geometrically fixed point with respect to the torso above the center of mass. Using VPP control, ATRIAS is able to take up to 22 steps on its own without using other techniques to keep its torso upright or inject energy, and it is shown that the generated ground reaction forces are similar to those produced by the reduced-order model. These controllers demonstrate that SLIP-like reduced-order control methods can be implemented on ATRIAS, and are a promising avenue for further research